I guess the PSU is indeed overloaded (assuming they really limited it to 120W): 7.5A * 22.5V = 168.75 W. However, I am unsure about the limit because I a) don't know the winding count of the transformer and b) don't have a eletronic load to test.
Check out this post for PSU details, maybe you have an idea? https://www.eevblog.com/forum/reviews/any-opinions-on-the-aixun-t3a/925/
I'm not sure that's the post you meant to link:
Oh well, yes, actually any sort of regularly turning power on/off is in fact "PWM". What I mean is that Aixun uses a PWM signal that is again turned on/off regularly, so low-freq PWM on a high-freq PWM signal.
EDIT2: Checking the output of the Unisolder with an oscilloscope for comparison could help... anyone?
EDIT3: Hmm... had a quick look, I might been wrong... maybe their PID algorithm is just weird or they use bad or non-optimal parameters. I wasn't able to full reverse-engineer it, yet
I'm familiar with posts below here as I noticed the correlation with the EE.SE post. PSU hasn't been discussed since, so I don't have a clue.
It seems to be pretty fast, anyway; responding within 100us is alright.
In fact, if it is indeed ramping up and down during and after the pulse, it sounds like pole-zero compensation, which means for short transients, the supply Zo is resistive. That is, for frequencies in the flat gain region above the zero, loop gain is fixed, i.e. some step change in Vo causes a proportional step change in converter input current, and thus output current, and so we expect some resistive delta Vo / delta Io for frequencies in this range, or pulses of comparable duration.
I'm assuming it's a basic TL431 regulated flyback.
Well, the "where" can be answered: Q4-1 (pin 1), heater transistor. See schematics https://github.com/c0d3z3r0/aixun_t3a_rev/blob/master/schematics/aixun_t3a.pdf
But what do you mean with "how"?
I don't know the board layout, I don't know how inductive it is, or what the CM noise might be like, what the probe ground clip looks like (length, orientation and where it's connected).
A key point for the control, given there's only one ground return wire in the handle, will be common mode due to cable inductance and resistance. Likely both are substantial. Hopefully it's either well enough filtered to avoid such errors, or sampled exclusive of the heating pulse; but the long time constant on the thermocouple amplifier might suggest otherwise. Another point in favor, on ramp-up it still makes noise, i.e. it doesn't drive at 100% duty.
Sampling too soon could easily be a cause of filtering/slow switching causing it to misread or error out. In other words, it depends on its hard switching as a design assumption.
Which further invalidates my EE.SE answer, but such information was never provided in the background to it (or maybe still isn't known at all, to any certainty that is, depending on how deeply the control has been probed, or if indeed the firmware has been extracted or decompiled). I probably delete the answer anyway, because anyone searching on the product issue will bring with them all the assumptions about the product itself, assumptions I never had.
Oh, did I ever link that? It was here...
https://electronics.stackexchange.com/questions/682699/pwm-circuit-that-switches-mosfet-with-soft-edgesI suppose it's just as well that it's closed, but Google will still find it.
Just an artifact that we can ignore, right?
Oh well, maybe the PSU was way to close to the scope... https://www.diyaudio.com/community/threads/smps-killed-my-radio-reception.373045/page-2
Well... maybe. I suppose it's not a functional problem at least. Maybe it's still a radiated or conducted issue. I wouldn't be surprised if it's untested.
It's certainly an ESD problem, not so much in terms of ESD per se, but the considerably lower impedance of the ground-return path, plus several volts of switching transients, isn't going to play well with anything that's grounded and also has diode junctions or whatever in it. You shouldn't be soldering on a plugged-in circuit anyway, but this is a likely assumption many will make regardless, and I think has already been noted in this or the other thread.
Easiest resolution would be changing to 24VAC (lower dI/dt, and, use whole-cycle switching), and run an independent ground wire (or combine it with the thermocouple but NOT the heater current). (Since we're talking response times of 100s ms, residual 50/60Hz can be notched out to further improve performance.) But, that's easy only on the conceptual design level. Far easier on a finished unit, considering ones' required labor input, to dump it in the trash and buy a better one... but y'all probably knew that already.
Put another way: you're very quickly running out of simple solutions (like fixing components or changing around filtering) that don't also involve updating the firmware.
The handle socket is aluminum? 
Try put a magnet on the leafs if you ever go there again and see if it's steel.
It's too bad china avoids copper and nickel-plating at all costs, giving us el crapola connections. We can't pay $1 more for a step up in quality?
Took apart the handle one more time and put a hard drive magnet right by the contact. No attraction at all. Looks and feels like Aluminium.
Ouch. Thanks for testing!
Eek. All the more reason to throw it out. I don't see any way a loose (well, sprung, give or take how tight it stays) aluminum contact handles, any current at all really, let alone the pulses here.
Tim
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